How to speed up the numerical integration with interpolation

General Usage Performance
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In this case the problem is that quadgk and scipy’s quad use different default tolerances.

Following the documentation, quadgk uses an absolute tolerance atol = 0 and relative tolerance rtol = sqrt(eps), while scipy’s quad uses the equivalent of atol = sqrt(eps) and rtol = sqrt(eps).

The default choice of quadgk is not the best in your case, as the analytical value of your integral is exactly zero. This is actually mentioned in the quadgk docs:

(Note that it is useful to specify a positive atol in cases where norm(I) may be zero.)

Choosing atol = sqrt(eps(Float64)) should bring the evaluation time close to the one you see in python.

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